Area Formulas
All area formulas give square units — cm², m², ft² — of whatever length unit you use.
2D shapes
| Shape | Area | Symbols |
|---|---|---|
| Square | s² | s = side |
| Rectangle | l × w | length, width |
| Triangle | ½ × b × h | base, perpendicular height |
| Triangle (3 sides) | √(s(s−a)(s−b)(s−c)) | s = half perimeter (Heron) |
| Circle | πr² | r = radius |
| Ellipse | πab | a, b = semi-axes |
| Trapezoid | (a + b)h ÷ 2 | a, b = parallel sides |
| Parallelogram | b × h | base, height |
| Rhombus / kite | pq ÷ 2 | p, q = diagonals |
| Sector | (θ/360)πr² | θ in degrees |
| Regular polygon | ns² ÷ (4 tan(180°/n)) | n sides of length s |
Surface areas of solids
| Solid | Surface area |
|---|---|
| Cube | 6s² |
| Box | 2(lw + lh + wh) |
| Cylinder | 2πr(r + h) |
| Sphere | 4πr² |
| Cone | πr(r + √(r² + h²)) |
Converting area units
Square the length factor: 1 m = 100 cm, so 1 m² = 10,000 cm². 1 ft = 12 in, so 1 ft² = 144 in². See the area conversion table.